You might want to look into some armor strip if you want to do damage to the grineer more quickly. Unairu operator, Saryn, Mag, Necros, Hildryn, Ember, Vauban, Xaku are some that can do it without augments. If you have access to helminth you can put something like Necros terrify on anybody and you're good to go.
For survivability, you can use certain frames or look into shield gating(augur mods and/or brief respite). What can also help quite a bit is jumping and rolling around - makes it so fewer bullets hit you.